Absolute Universal Swan Song

People keep composing "new" melodies. How long will this keep going on? (Isn't that the name of a song?) I know some of these melodies are the same, and others are nearly the same. Has anyone calculated, within a reasonable set of limitations on variance (according to Western esthetic musical criteria), both extensively and differentially, just how many melodies are possible, after which comes the day the music dies?

OK, so it's a stupid question, but I bet Marilyn Vos Savant would have an answer, so Cece ought to.

Raymond A. Chamberlin
raych@tsoft.net

It seems like I read somewhere what the total number of possible melodies are, but I forget the amount.

The thing to remember is that western music ("western" meaning European and European inspired music, including American) has a set of rules that it goes by. These involve things like "keys", "meters", and "form". There has been some experimental work done on music that departs from these rules and follow a different set of rules. (Rules are necessary, or else it stops being music and becomes noise.) However, these experiments have been somewhat limited by the fact that the masses don't seem to like them.

I guess what I'm trying to say, is that there is still plenty of fresh territory. It just takes a lot of time for it to become popular.

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Carpe hoc!

Rules are NOT necessary, if they were there'd be no progress. What happens is someone creates something and people go "hey, that's good, how can we repeat that? " People are always trying to explain art then acting like the rules created the quality, major bullshit,
Larry

Rules are necessary to answer the question. If you think that there are infinitely many sounds that can make up a melody, then obviously there are infinitely many ways to combine them.

If the "rules" of a melody starts with (say) eighty-eight "sounds" on the piano, and a melody is defined as some combination of those sounds, through the use of ten or eleven different meters (I assume that transposition of key wouldn't produce a different melody) then there are a finite (though very large) number of melodies.

The biggest barrier to being able to answer the question is "length" -- how many sequential tones, max, may a sequence of sound go without repeating itself and thereby constitute a melody? If we agree on, say, 240 tones, we can use math to determine the number of available combinations. Since most such combinations would sound like random noise, we could apply other rules, which would lower the answer considerably.

But who gets to determine that, for instance, Richard Strauss' Also Sprach Zarathustra, which runs maybe 45 minutes or thereabouts without repeating tonal motifs or previous musical phrases, does not constitute a melody? It would be pretty arbitrary, wouldn't it?


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Designated Optional Signature at Bottom of Post

If you set an infinite number of monkies loose in an infinite orchestra pit for an infinite amount of time, would they eventually play Mahler's 5th? Oh, you said melody.

"Melody" means different things to different people. The answer to this question depends completely on one's subjective opinion as to what constitutes one.

My father's definition is "a tune you can whistle" and that leaves out a ton of stuff popularly described as music but would include any series of random notes one thought pleasant and could memorize.

Merriam Webster says:
1 : a sweet or agreeable succession or arrangement of sounds : TUNEFULNESS
2 : a rhythmic succession of single tones organized as an aesthetic whole

The word "aesthetic" blows this question out of the water, in my opinion.

Ivick - Progress isn't made by completely breaking the rules, just by pushing at the boundaries.

I was going to link to an album on CDnow which has music from a different rule set, namely arabic. But the url is too long to post here (grrr) so I am just going to recommend that if you want to hear something different, search for the artist "Tekbilek" in CDnow, then select the album Gypsy Fire and the song Rompi Rompi

Larry, I'm not saying the rules don't change. If they didn't we'd still be chanting in perfect fourths and fifths. But as other posters have mentioned, the boundaries get pushed. As they do, the rules change. In Handel's day, an Am9 chord would have been very unusual. Today, it's almost passe. However, there are still rules on how it is to be used.

Keep in mind, I'm saying "rules", not "laws".

What I mean by "rules being necessary" is that there must be some sort of pattern for a piece of music to be music. Something to make it sound "created", "meaningful", or at least "intentional".

I think I remember someone calculated the number of possible notes and their different possible configurations. Then based on the number of songs produced per year he determined when we would have run out of new combinations. I think he determined we would run out of new songs by 1973.

That would certainly explain the pop charts for the past couple decades.

You're right there.

Here's a paper on extracting and comparing melodies at:

http://www.acm.org/sigmm/MM98/electronic_proceedings/uitdenbogerd/index.html

I remember trying, during undergraduate college, to make -- with tubes, back before there were transistors or ICs (well, at least at a reasonable price) -- a circuit that would extract the melody from a musical piece played on the radio, by clipping, clamping and linearly filtering. Results weren't too great, to say the least. Shouldn't be much of a trick to do it now from MIDI files -- and then, after scaling a few parameters -- compare them for similarity.

Take ordinary French-ballad-style pop tunes in sections of form 'AABA', limited to 1.5 octaves, melody that will follow a reasonable chord progression and resolve properly. Subtle differences don't count -- 1 quarter note vs. 2 eighth notes or dotted eighth and sixteenth notes, both at the same pitch, etc.; shifts of melody wrt to beats; octaval substitutions; whatever. Shouldn't be *too* many permutations.

I think sometimes, though, that the melodies of some songs sound a lot alike to me, while not being all that close; e.g., "From a Distance" and "From This Moment On".

Think I could get any money for an MP3 that would take a tune out of your head that's been going around in it too long? One that has the particular melody subtracted from white noise? ;-)

Ray

What I mean by "rules being necessary" is that there must be some sort of pattern for a piece of music to be music. Something to make it sound "created", "meaningful", or at least "intentional".

4'33"

Subtle differences don't count -- 1 quarter note vs. 2 eighth notes or dotted eighth and sixteenth notes, both at the same pitch, etc.; shifts of melody wrt to beats; octaval substitutions; whatever. Shouldn't be *too* many permutations.

I think a problem here is that each limitation moves the answer set further from the musical realm and further into that of pure permutation calculation. The question becomes related to music in only that it takes a few selected parameters and plugs them into an equation.

I also submit that if one considers any of the above proposed limitations as "subtle", they are very poor musicians.

Spider Robinson wrote a story based on this idea, Melancholy Elephants.

Ah yes. 4'33". One of my favorite pieces. John Cage, wasn't it. BTW, if you're implying there isn't a rule, remember it is 4'33" long, and the performer must not do anything. Simple rules, but they still exist.

(Of course, there is some debate as to whether or not it qualifies as "music".)

My opinion is that for most practical purposes, it's infinite.

I play classical piano, so here's what I recommend if you want to get a feel for how varied melodies can be. Listen to a good recording of something like Chopin's Opus 28 No 16 - there is an extraordinary degree of subtle complexity there which I have never heard approached in modern popular music. After listening to this type of piece, it sure seems like most music only uses a fraction of the available "complexity-space", even if you discount variables such as different instruments, dynamics, and so on.

Chopin tends to use devices such as 22-nd notes set against 8-th notes, and rapid many-octave arpeggios used almost as a single musical unit, with dynamics varying throughout, and these arpeggios then vary in facinating ways as the song progresses so that one gets an impression of almost a liquid sort of movement throughout the course of the song. "Genius" is the only word that comes to mind to describe his work, although there are not many musicians in the world who can do justice to it.

I think even within the style of one composer, there is almost infinite room for musical variation.

I don't think we'll ever run out of melodies.

k0myers

Mrknowitall: What you said was rules are necessary to call it music and not noise. And I challenge that, rules are used by the mediocre to emulate the truly creative. The reason we use the Am9 is because someone said "I don't care if it breaks the rules, it's music to me."

And BTW it's Lvick,
Larry

I think things have slipped here more than a little with kOmyers and lvick. The discussion here was set out to be limited to basic melodies, not entire musical compositions, and in respect to the former, the idea was only to limit subtleties in them just for the purpose of distinguishing them. I hardly had any intention of reducing Frederic Chopin to a one-fingered MIDI-file sequencer. I can especially appreciate all the intricate nuances of this composer, but classical music borrows (?) themes from peasant music, and the modern popular music steals (?) melodies from the classics. A theme or melody is recognizable, much as is the Mona Lisa, whether it be in the Louvre (or wherever the original is supposed to be) or in a tatoo on the bottom of someone's foot.

I disagree with lvick, when he says,

. . .rules are used by the mediocre to emulate the truly
creative.

That, of course, is attempted from time to time, but rules are also used by the mediocre to simply *analyze* the masterworks of the "truly creative", for the purpose of appreciating many of the types of subleties that make up musical masterpieces. I only mentioned rules in their possible role of ferreting out identical or similar thematic threads within different musical compositions, which threads could be regarded as the same melodies.

Certainly, no one can deny the spendidness, distinctness and intracy of Chopin's arpeggios; but, although they are essential to his unmatched style, and are integrated supremely with the other facets of his works, *they* do not constitute the essence of the *melodic themes* of his compositions.

kOmyers states:

Chopin's
Opus 28 No 16 - there is an extraordinary degree of subtle complexity there which
I have never heard approached in modern popular music.

True, that complexity makes the piece as a whole a work of only Chopin, and such involved manipulations don't occur in popular music, but. . .while remembering that what we're up to is trying to distinguish different melodies and lumping the same ones. . .let's take, for instance, Chopin's "Fantasie Impromptu", Opus 66. Go to:

http://www.tsoft.net/~raych/Melodies.htm

On this ad-hoc page of mine, you will find first (if the lawyers haven't beforehand) an MP3 of a professional rendition of this piano piece. Below that you will find a MIDI sequence of the same piece, which of course, lets Chopin down a good bit. Finally, you will find another, really lousy MIDI file of "I'm Always Chasing Rainbows", the old popular song that was taken from this work of Chopin. In this particular, almost unrecognizable, thumped-out synthesis of the song, there is still what must be admitted to be the same basic melody as found in part of Fantasie Impromptu (except for a few bars at the ends of some passages). Same thing with the old popular tune, "Till the End of Time" and another work of Chopin.

Of course, in bringing up this matter of a limitation in the number of truly distinct melodies, I hadn't intended to bother M. Chopin, but now maybe I've gotten his various body parts rolling over in whatever locations they're in these days. I was merely trying to deal with possibilities in popular tunes, but things always seem to get so complicated around this message board.

The piece I used to like to try to play was his "Nocturne", Op. 9, No. 2. You should be glad I didn't try to produce my attempts at *that* on my referenced page.

Ray (There are really only as many as there are "pretty girls", I suppose.)

To fix my link:

http://www.tsoft.net/~raych/Melodies.htm

Ray

Sorry, too late at night. Voilà:

http://www.tsoft.net/~raych/Melodies.htm

Ray

Nanobyte writes, "Certainly, no one can deny the spendidness, distinctness and intracy of Chopin's arpeggios; but, although they are essential to his unmatched style, and are integrated supremely with the other facets of his works, *they* do not constitute the essence of the *melodic themes* of his compositions."

Hmm. Interesting. I think I'm missing some subtlety of what you're asking, but I'm not sure exactly what. Anyway:

The way I look at it is: Chopin's arpeggios (at least sometimes) do constitute a "melodic theme", since his songs are often build with some sort of arpeggio as a "unit", and not only does the starting point move around over the course of the song, but the note progression in the arpeggio changes in a way that is essential to the character of the song. It would sound completely different if, say, in Opus 28 No 18, you started the decending arpeggios on the same notes, but used a different series of notes within.

Maybe I'm not understanding your idea of what a "melody" is? I definately agree that there are popular pieces which, err, "borrow" themes from classical music. But since the number of truely distinct melodies just in classical music alone (without even touching on jazz or other genres) seems so vast, and modern classical composition doesn't seem to have any trouble coming up with new and distinct ones, it seems like we haven't even really scratched the surface.

Here's another slightly different way to look at it. Let's ignore for a moment the distinction between "music" and "a random series of notes" (and one could argue that a lot of music does ignore this distinction :-) ). Having removed that distinction for now, let's say we have a piano with 88 notes, and a "melody" can be any series of notes up to, say, 100 notes in length (in classical music, I think that melodic themes sometimes exceed this, but I'm just making numbers up here). This gives us an upper bound of exp(88,100) ways to arrange those notes, and that's neglecting note lengths entirely, and it's neglecting chords and quite a few other things as well.

Well, clearly a large fraction of that space is flat out unmelodic - it would sound just like random notes. But 88^100 is a staggeringly huge number - even a miniscule percentage of this space which is melodic could easily still be mind-numbingly huge. So it isn't very hard for me to imagine that there are a LOT of different melodies one could come up with that sounded "good".

On the other hand, having myself tried to compose music, I'm pretty sure all of the available melodies have already been taken :-)

k0myers

The debate over whether there were rules in music sounds like a great GD topic. So, heck, I started one:

http://www.straightdope.com/ubb/Forum7/HTML/000176.html


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Carpe hoc!

Aw, c'mon, kOmyers, are we supposed to believe that folks in the hills know what a tune/melody/theme/whatever is, but that anyone getting into sophisticated classical music rapidly forgets what such a thing is? You keep going back to classical music. Classical music may, in some cases, just be exercises in embellishment, but I believe most of its well-known works center on one or more melodic themes. However, my original posted question really contemplated dealing only with popular tunes, which continue to be churned out at quite a rate, though maybe slowing some, after a good, solid, rapid-fire century, and very many tunes before having come about before that. Many, many of them bear the same names. That is trivial to verify. But also, quite a number of these tunes seem to me to be very close to being the same tune -- if not exactly so. Can't we simply forget classical music and all its elaborations for the time being, and deal with those things we can easily whistle, as another poster put it?

Now, 88^100 in no way deals with my question. First off a piano is only one of the many instruments that can be used to play a tune, and not all of them have 88 keys. And the number of keys on any real instrument, or some equivalent chosen in synthetic music, is irrelevant -- for one reason, because the same note may be used anywhere in the sequence of a tune, including any number of adjacent positions. But, worst, the basic idea in this gross approach gives, as you mention, a tremendous portion of its "tune space" to nothing but totally unmusical, random or over-patterned garbage. Tunes are played on particular scales, within pitch limits much less than the extremes of some instruments, such as pianos, on which they are played. Tunes repeatedly wander off in 'tension' and then resolve to pitches of set ratios to those on which they start.

Various types of fences can be put around all but the most exotic music, without imposing more than reasonable constraints on their tunes. I once looked into the pitches "naturally" chosen by 1/f noise (so-called "pink" noise) (obtainable naturally from semiconductors or otherwise mathematically), with which a physics PhD who stayed at my house was experimenting at the time. The note sequences chosen by this noise compare quite closely to those found in classical music. (Hey, how did we get back to that? But part of Chopin's genius was due to 1/f noise in his head.) However, 1/f noise knows nought at all of the resolution of themes, because it pays no attention to any key. Additionally, rythm and phrase constraints are necessary to shape popular tunes of the non-exotic, harmonic type. You have to set up wide-ranging, but not unlimited, fences on those parameters, in order to corral all reasonable romantic tunes. You can't just build what is almost a Christo fence ( http://people.a2000.nl/ttijen/MAPENG.html ); you have to make it include only the green grass and water holes.

Anyhow, we gotta find some way to arm the melody police. . .so that we don't get taken by tunes that have been crunched out at least several times before under different names. ;-) I think tunes're like area codes; you can't just keep dumping them out forever.

Ray (OK, so after a while, you get a little out of tune.)

NanoByte says, "You keep going back to classical music"

Well, the original post only mentioned "Western esthetic music criteria", so I figured it was fair game to include classical/jazz/etc, since it avoids the problem you pointed out of repetition in popular music, and there is active composition in both. But ok, we can discard those genres for the purpose of the question if you'd like.

NanoByte also writes, "But also, quite a number of these tunes seem to me to be very close to being the same tune"

Certainly. But is this because we're running out of tunes? It'll take quite a lot to convince me of that one :-). I think it's due to other factors; musical influence of earlier generations, knock offs done intentionally, remakes of old songs, new songs that were composed right after the musician had heard some older song on the radio, "borrowing" a phrase from an older song for effect, or whatever else.

NanoByte says, "First off a piano is only one of the many instruments that can be used to play a tune..."

Can't disagree there :-). But since the question was pondering how long new tunes can be cranked out, no? Certainly it is possible to play tunes on a piano. It stands to reason that to answer this question, one would want to look at a versatile instrument, not a restrictive one. You can probably find an instrument somewhere that can only play one note, but does that mean we ran out of tunes right after we invented it? You don't run out of tunes until you run out on the least restrictive instrument.

"within pitch limits much less than the extremes of some instruments, such as pianos, on which they are played"

Ok, I'm still trying to get a handle on what you consider a tune. For my definition, I have music for tunes that uses both the very bottom and the very top note on my piano, and all in between, and they sure sound like tunes to me. But ok: let's say that it's not a tune if it uses very high or low notes. (I'm not being sarcastic here, just trying to understand your notion of a tune, which seems to get more restrictive all the time :-) ).

NanoByte writes, "Now, 88^100 in no way deals with my question"

Ok, fair enough - it's your question! But I think you need to define the question better. For instance, it seemed perfectly reasonable to me to include tunes that could be played on a piano as potential "new melodies", but that doesn't seem to fit in with the spirit of your question. I'm honestly not trying to be obtuse here; i'm interested in the topic too, and I'm trying to understand the spirit of your question.

I think that even under a very strict set of rules (say, notes from no more than 3 octaves, no jazz or classical like progressions, a tune can be no longer than 25 notes, rythym doesn't count, etc), the number of potential musical sounding tunes is still huge. I mean really truely vast. But tell me concretely what the rules are for a "tune", and maybe between us we can come up with a more concrete WAG.

k0myers